Modeling And Analysis Of Mitigating The Transmission Of Zika Virus

This work is mainly study how Wolbachia-infected males control the transmission of Zika virus and the role of sexual transmission in Zika virus transmission in the deterministic and stochastic settings.For the determination model,this work defines the threshold for the offspring of the wild mosquito population.Based on the threshold of mosquito population offspring,we obtain the basic reproduction number of disease by the next-generation matrix approach,and analyze the stability of disease-free equilibrium by Hurwitz criterion and Lyapunov function.Finally,this work evaluates the impact of the parameters on the basic reproduction number by sensitivity analysis.Numerical simulations show the time it takes for mosquito populations to go extinct,and the upper and lower bounds for the relative release rate of Wolbachia-infected male mosquitoes to be cost effective.This work incorporates the impact of environmental white noise on death rates of aquatic stage of mosquitoes,adult mosquitoes,and humans to develop a stochastic model for Zika virus.For the stochastic model,this work proved that this model has a unique and bounded global solution and derived the sufficient conditions for the extinction of Zika virus.Finally,this work proved the existence of a unique ergodic stationary distribution of the solutions by constructing Lyapunov function.Numerical simulations show that the white noise may drive the disease to extinction when the intensity of the white noise is large enough,and the release of Wolbachia-infected mosquitoes shortens the time it takes for the wild mosquitoes to become extinct.